Sharpe Ratio Information Coefficient

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Description

Computes the Sharpe Ratio Information Coefficient of Paulsen and Soehl, an asymptotically unbiased estimate of the out-of-sample Sharpe of the in-sample Markowitz portfolio.

Usage

1
sric(z.s)

Arguments

z.s

an object of type sropt

Details

Let X be an observed T x k matrix whose rows are i.i.d. normal. Let mu and Sigma be the sample mean and sample covariance. The Markowitz portfolio is

w = Sigma^-1 mu,

which has an in-sample Sharpe of zeta = sqrt(mu' Sigma^-1 mu).

The Sharpe Ratio Information Criterion is defined as

SRIC = zeta - ((k-1) / (T zeta)).

The expected value (over draws of X and of future returns) of the SRIC is equal to the expected value of the out-of-sample Sharpe of the (in-sample) portfolio w (again, over the same draws.)

Value

The Sharpe Ratio Information Coefficient.

Author(s)

Steven E. Pav shabbychef@gmail.com

References

Paulsen, D., and Soehl, J. "Noise Fit, Estimation Error, and Sharpe Information Criterion." arxiv preprint (2016): http://arxiv.org/abs/1602.06186

See Also

Other sropt Hotelling: inference

Examples

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# generate some sropts
nfac <- 3
nyr <- 5
ope <- 253
# simulations with no covariance structure.
# under the null:
set.seed(as.integer(charToRaw("fix seed")))
Returns <- matrix(rnorm(ope*nyr*nfac,mean=0,sd=0.0125),ncol=nfac)
asro <- as.sropt(Returns,drag=0,ope=ope)
srv <- sric(asro)

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